By Horst-Heino Borzeszkowski, H.J. Treder
In discussing the query of even if common Relativity concept fairly has to be quantized, a easily adverse solution can't be authorised, after all. Such a solution isn't gratifying simply because, first, Einstein's gravitational equations attach gravity and non-gravitational topic and since, moment, it may be taken without any consideration that non-gravitational subject has an atomic or quantum constitution such that its energy-momentum tensor status at the right-hand part of Einstein's equations is shaped out of quantum operators. those proof make it very unlikely to learn the left-hand aspect of Einstein's equations as a normal classical functionality. this doesn't inevitably suggest, notwithstanding, that we needs to draw the belief that normal Relativity idea, just like electrodynamics, may possibly or could be quantized in a rigorous demeanour and that this quantization has related results to quantum electrodynamics. In different phrases, whilst for purposes of consistency quantization is attempted, then one has to invite no matter if and the place the quantization process has a actual that means, i.e., even if there exist measurable results of quantum gravity. IQ accordance with those questions, we're quite often facing the discus sion of the rules of quantized common Relativity conception and with the estimation of quantum results together with the query in their measurability. This research proves that it really is most unlikely to differentiate among classical and quantum normal Relativity idea for the extraordinary case of Planck's orders of value. In different phrases, there doesn't exist a bodily significant rigorous quantization perception for Einstein's theory.
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Extra resources for The Meaning of Quantum Gravity
At any rate, this is true for the limitations given by Heisenberg's uncertainty relations. These relations also restrict the validity of 39 Measurement in Quantum Gravity the Ehrenfest theorem. Therefore, the above-given argument based on this theorem is nontrivial as far as it presupposes that, despite Heisenberg's uncertainty relations, a classical measurement can be realized with an, in principle, unlimited accuracy. To clarify to what extent this presupposition is justified, we shall discuss quantum nondemolition measurements from the viewpoint of principles of measurement discussed above (we follow here von Borzeszkowski and Treder, 1983a).
The covariant quantization of the gravitational field uses the functional integral formulation of quantum field theory (DeWitt, 1964; Faddeev and Popov, 1973). 24) where g#v denotes the Riemannian metric of the spacetime manifold. The Lagrangian density is given by the Ricci scalar Lgrav = R. Following the Faddeev-Popov formalism of quantized gauge fields (Faddeev and Slavnov, 1978), the functional integral is to be carried out over all nongauge equivalent classical field configurations. This is realized by choosing a section of the gauge group which intersects all orbits of the group one times.
The reference metric g~v and the metric gpv transform both as tensors with respect to coordinate transformations. This means that, in order to ensure coordinate covariance, action integrals have to be scalars constructed from g~v and gpv' As a gauge group the Einstein group acts on gpv alone, g~v remains fixed. 26) specifying gpv with respect to g~v' Examples of this kind are given by Adler (1982). The scheme must be completed by the proof that the chosen gauge is an allowed one (Faddeev and Slavnov, 1978).
The Meaning of Quantum Gravity by Horst-Heino Borzeszkowski, H.J. Treder